Security Device Including Physical Unclonable Function Cells, Operation Method of Security Device, and Operation Method of Physical Unclonable Function Cell Device

ABSTRACT

A security device includes a physical unclonable function (PUF) cell array that includes a plurality of PUF cells connected with a first word line, a controller that selects a target PUF cell of the plurality of PUF cells and outputs a control signal based on the target PUF cell, a decoder that applies a first voltage to the first word line in response to the control signal, a bit line selection circuit that outputs a target current across a bit line connected with the target PUF cell and a sum current corresponding to a sum of currents across the remaining bit lines connected with other PUF cells, and a bit determiner that outputs a target bit of the target PUF cell based on the target current and the sum current, and the security device generates a security key based on the target bit for responding to an authentication requests.

CROSS-REFERENCE TO RELATED APPLICATIONS

This U.S. non-provisional patent application is a division of U.S.application Ser. No. 16/994,078, filed Aug. 14, 2020, which claimspriority under 35 U.S.C. § 119 to Korean Patent Application No.10-2019-0138808 filed on Nov. 1, 2019, in the Korean IntellectualProperty Office, the disclosures of which are incorporated by referenceherein in their entireties.

BACKGROUND 1. Technical Field

Embodiments of the inventive concept disclosed herein relate to asecurity device, and more particularly, relate to a security deviceincluding physical unclonable function (PUF) cells, an operation methodof the security device, and an operation method of a physical unclonablefunction cell device.

2. Discussion of Related Art

Technologies associated with security and encryption are important forcommunication devices and mobile devices. In cryptography, a key is apiece of information that determines the functional output of acryptographic algorithm. When the key is generated using software on asystem connected to a network, a non-authorized user can gain access tothe key by hacking into the system. Thus, hardware-based securitytechnologies are being developed.

A physical unclonable function (PUF) based security device generates aunique key randomly based on process, voltage, and temperature (PVT) ofthe device. However, an error may occur in the key due to variousenvironmental factors. This error reduces the reliability of the PUFdevice.

SUMMARY

At least one exemplary embodiment of the inventive concept provides asecurity device including physical unclonable function (PUF) cellshaving improved reliability and reduced circuit complexity, an operationmethod of the security device, and an operation method of a physicalunclonable function cell device.

According to an exemplary embodiment, a security device includes aphysical unclonable function (PUF) cell array that includes a pluralityof first PUF cells connected with a first word line, a controller thatselects a target PUF cell of the plurality of first PUF cells andoutputs a control signal indicating the selected target PUF cell, adecoder that applies a first voltage to the first word line in responseto the control signal, a bit line selection circuit that is connectedwith a plurality of first bit lines and outputs a first target currentacross a bit line connected with the target PUF cell from among theplurality of first bit lines and a first sum current corresponding to asum of currents across the remaining bit lines connected with other PUFcells from among the plurality of first PUF cells, and a bit determinerthat outputs a target bit of the target PUF cell based on the firsttarget current and the first sum current, and the security devicegenerates a security key based on the target bit for responding to anauthentication request.

According to an exemplary embodiment, an operation method of a physicalunclonable function (PUF) cell device which includes a plurality ofphysical unclonable function (PUF) cells includes selecting a target PUFcell of the plurality of PUF cells, applying a first voltage to a firstword line connected with the target PUF cell, generating a target valuebased on a target current corresponding to the target PUF cell andgenerating a central value based on a sum current corresponding to a sumof currents output from other PUF cells connected with the first wordline, determining a target bit of the target PUF cell based on thetarget value and the central value, and generating a security key basedon the target bit for responding to an authentication request.

According to an exemplary embodiment, an operation method of a securitydevice including first to N-th physical unclonable function (PUF) cellsincludes applying a first voltage to a first word line connected withthe first to N-th PUF cells, obtaining first information from the firstPUF cell and obtaining second information from the second to N-th PUFcells, determining a first bit of the first PUF cell from the obtainedfirst information and the obtained second information, applying thefirst voltage to the first word line connected with the first to N-thPUF cells, obtaining third information from the second PUF cell andobtaining fourth information from the first and third to N-th PUF cells,determining a second bit of the second PUF cell based on the obtainedthird and fourth information, and generating a security key based on thefirst bit and the second bit for responding to an authenticationrequest, where N is a positive integer.

BRIEF DESCRIPTION OF THE FIGURES

The inventive concept will become apparent by describing in detailexemplary embodiments thereof with reference to the accompanyingdrawings.

FIG. 1 is a block diagram illustrating a security device according to anexemplary embodiment of the inventive concept.

FIG. 2 is a diagram for describing a method of determining a target bitof a PUF cell.

FIG. 3 is a block diagram illustrating a PUF cell device of FIG. 1according to an exemplary embodiment of the inventive concept.

FIG. 4 is a diagram illustrating an exemplary structure of a pluralityof PUF cells of FIG. 3 .

FIG. 5 is a diagram illustrating a configuration of a PUF cell device ofFIG. 3 according to an exemplary embodiment of the inventive concept.

FIG. 6 is a flowchart illustrating an operation of a PUF cell device ofFIGS. 3 and 5 .

FIG. 7 is a diagram for describing an operation of a PUF cell device ofFIG. 3 .

FIG. 8 is a diagram for describing a target bit determining method of aPUF cell device of FIG. 3 according to an exemplary embodiment of theinventive concept.

FIG. 9 is a diagram illustrating a PUF cell array according to anexemplary embodiment of the inventive concept.

FIG. 10A is a diagram illustrating an exemplary PUF cell device to whicha PUF cell array of FIG. 9 is applied.

FIGS. 10B to 10D are diagrams for describing an operation of a PUF celldevice of FIG. 10A according to an exemplary embodiment of the inventiveconcept.

FIG. 11 is a diagram for describing a way to improve reliability of aPUF cell device.

FIG. 12A is a flowchart for describing an operation of an unstable PUFcell or a valid PUF cell of a PUF cell device of FIG. 1 according to anexemplary embodiment of the inventive concept.

FIG. 12B is a diagram for describing an operation of an unstable PUFcell or a valid PUF cell of a PUF cell device of FIG. 1 .

FIGS. 13A and 13B are diagrams for describing an operation according tothe flowchart of FIG. 12A.

FIG. 14 is a block diagram illustrating a controller of FIG. 1 accordingto an exemplary embodiment of the inventive concept.

FIG. 15 is a diagram for describing an operation of a PUF cell deviceaccording to an exemplary embodiment of the inventive concept.

FIG. 16A is a block diagram for describing an operation of a securitydevice according to an exemplary embodiment of the inventive concept.

FIGS. 16B and 16C are flowcharts for describing an operation of asecurity device according to an exemplary embodiment of the inventiveconcept.

FIG. 17 is a block diagram illustrating an electronic system to which asecurity device according to an exemplary embodiment of the inventiveconcept is applied.

FIG. 18 is a block diagram illustrating an electronic device to which asecurity device according to an exemplary embodiment of the inventiveconcept is applied.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

Below, embodiments of the inventive concept may be described in detailand clearly to such an extent that one of an ordinary skill in the artcan implement the inventive concept.

Components described in the detailed description with reference to terms“part”, “unit”, “module”, “layer”, etc. and function blocks illustratedin drawings may be implemented in the form of software, hardware, or acombination thereof. For example, the software may be machine code,firmware, an embedded code, and application software. For example, thehardware may include an electrical circuit, an electronic circuit, aprocessor, a computer, an integrated circuit, integrated circuit cores,a pressure sensor, an inertial sensor, a microelectromechanical system(MEMS), a passive element, or a combination thereof.

Also, unless differently defined, all terms used herein, which includetechnical terminologies or scientific terminologies, have the samemeaning as that understood by a person skilled in the art to which theinventive concept belongs. Terms defined in a generally used dictionaryare to be interpreted to have meanings equal to the contextual meaningsin a relevant technical field, and are not interpreted to have ideal orexcessively formal meanings unless clearly defined in the specification.

Below, to describe the inventive concept, a number of exemplarycomponents or exemplary numerical values are provided, but the inventiveconcept is not limited thereto. For example, in drawings below, forbrevity of illustration, an example of eight PUF cells connected to oneword line is illustrated. However, the inventive concept is not limitedthereto since this example is merely for describing the inventiveconcept.

FIG. 1 is a block diagram illustrating a security device according to anexemplary embodiment of the inventive concept. FIG. 2 is a diagram fordescribing a method of determining a target bit of a PUF cell. Ahorizontal axis of a distribution of FIG. 2 indicates information (e.g.,mismatch information or an amount of current) obtained from PUF cells.Referring to FIGS. 1 and 2 , a security device 10 includes anarray-based physical unclonable function (PUF) cell device 100 (e.g., asemiconductor device) and a controller 101 (e.g., a control circuit).

The array-based PUF cell device 100 may include a plurality of PUFcells. The plurality of PUF cells may be arranged in the form of anarray. Below, for convenience of description, the array-based PUF celldevice 100 is simply referred to as a “PUF cell device 100”.

In an exemplary embodiment, each of the plurality of PUF cells may beimplemented with at least one of various kinds of PUF cells such as aPUF cell based on a threshold voltage of a transistor, an arbiter-basedPUF cell (e.g., a feed-forward PUF cell, an XOR PUF cell in whicharbiter PUF cells are arranged in parallel, or a lightweight PUF cell),a ring oscillator-based PUF cell, a memory-based PUF cell (e.g., astatic random access memory (SRAM) PUF cell, a latch PUF cell, a flashmemory PUF cell, or a memistor PUF cell), and a PUF cell reconfigurableaccording to a laser beam or a thermal variation.

Below, to describe the inventive concept, it is assumed that each of theplurality of PUF cells is a PUF cell based on a threshold voltage of atransistor. However, the inventive concept is not limited thereto. Forexample, each of the plurality of PUF cells may be implemented withvarious types of PUF cells.

The PUF cell device 100 is configured to output a target bit TB undercontrol of the controller 101. The controller 101 controls the PUF celldevice 100. For example, the controller 101 provides a control signalCTRL to the PUF cell device 100. The control signal CTRL may includeinformation or an address for selecting a target PUF cell of theplurality of PUF cells included in the PUF cell device 100. For example,the control signal may uniquely identify the target PUF cell.

The PUF cell device 100 may select the target PUF cell of the pluralityof PUF cells in response to the control signal CTRL received from thecontroller 101 and may output the target bit TB corresponding to theselected target PUF cell.

The controller 101 may receive target bits TB associated with all orsome of the plurality of PUF cells included in the PUF cell device 100and may generate and output a security key KEY based on the receivedtarget bits TB.

In an exemplary embodiment, the plurality of PUF cells may havedifferent process, voltage and temperature (PVT) variations. Even thoughthe same bias (e.g., a bias current, a bias voltage, etc.) is providedto the plurality of PUF cells, each of the plurality of PUF cells mayoutput different information depending on the corresponding PVTvariation. For example, even though the plurality of PUF cells aremanufactured by the same semiconductor process or on the same wafer, theplurality of PUF cells may have different PVT variations due to variousfactors (e.g., doping concentration, a thickness of a gate oxide layer,and a geometrical structure).

That is, even though a first PUF cell and a second PUF cell aremanufactured by the same semiconductor process or on the same wafer,information output from the first PUF cell may have a positive polarity,and information output from the second PUF cell may have a negativepolarity. Alternatively, the size or the value of the information outputfrom the first PUF cell and the size or the value of the informationoutput from the second PUF cell may be different.

A target bit TB associated with each of the plurality of PUF cells maybe determined based on the information of each of the PUF cells. Forexample, pieces of information output from the plurality of PUF cellsincluded in the PUF cell device 100 may form a first distribution DB1illustrated in FIG. 2 . In an exemplary embodiment, the firstdistribution DB1 may be a Gaussian distribution or a normaldistribution. A central value (e.g., a peak) of the first distributionDB1 may be used as a reference value REF0 for determining a polarity ofeach of the plurality of PUF cells. For example, a PUF cell havinginformation less than the central value can be considered to have anegative polarity and having information greater than or equal thecentral value can be considered to have a positive polarity.

An exemplary PUF cell device determines a target bit of a target PUFcell by collecting analog information of the target PUF cell, convertingthe collected analog information into digital data through ananalog-to-digital converter, and comparing the converted digital datawith reference data (i.e., the reference value REF0).

However, the PUF cell device 100 according to an exemplary embodiment ofthe inventive concept determines the target bit TB of the target PUFcell without using a separate analog-to-digital converter and separatereference data. For example, the PUF cell device 100 according to anexemplary embodiment of the inventive concept may determines the targetbit TB by generating or calculating a central value based on other PUFcells corresponding to the target PUF cell from among the plurality ofPUF cells and comparing a target value corresponding to the target PUFcell and the central value. A structure and an operation of the PUF celldevice 100 according to an exemplary embodiment of the inventive conceptwill be described with reference to drawings below.

FIG. 3 is a block diagram illustrating a PUF cell device of FIG. 1according to an exemplary embodiment of the inventive concept. Forbrevity of illustration, an example is illustrated as a plurality of PUFcells PC are arranged in an 8×8 matrix, but the inventive concept is notlimited thereto. A PUF cell array 110 may further include additional PUFcells, and thus, the number of word lines and the number of bit linesmay increase. In an exemplary embodiment, the number of PUF cells PCconnected to one word line is at least “N”. In this case, “N” indicatesthe minimum number of PUF cells, of which values form a normaldistribution or a Gaussian distribution. In an exemplary embodiment, “N”may range from 4 to 256.

For convenience of description, it is assumed that information obtainedfrom each of the plurality of PUF cells PC is a current generatedaccording to a word line bias of each of the plurality of PUF cells PC.However, the inventive concept is not limited thereto. For example,information obtained from a PUF cell may be variously changed ormodified depending on a type of the PUF cell.

Referring to FIGS. 1 and 3 , the PUF cell device 100 includes the PUFcell array 110, a decoder 120 (e.g., a decoder circuit), a bit lineselection circuit 130, a bit determiner 140 (e.g., a circuit), and avoltage regulator 150.

The PUF cell array 110 includes the plurality of PUF cells PC. Theplurality of PUF cells PC may be arranged in a row direction and acolumn direction to form an array. The plurality of PUF cells PC may beconnected with a plurality of word lines WL1 to WL8 and a plurality ofbit lines BL1 to BL8. Each of the plurality of PUF cells PC may beconfigured to output a current depending on a bias (e.g., a biascurrent, a bias voltage, etc.) of the corresponding word line of theplurality of word lines WL1 to WL8. As described above, a current thatis output from each of the plurality of PUF cells PC may have a valuethat varies depending on a physical characteristic or an ambientcondition of each of the plurality of PUF cells PC.

The decoder 120 receives and decodes the control signal CTRL from thecontroller 101. For example, the control signal CTRL may include addressinformation corresponding to a target PUF cell, of which the target bitTB is to be determined, from among the plurality of PUF cells PC. Thedecoder 120 decodes the address information corresponding to the targetPUF cell and controls the plurality of word lines WL1 to WL8, based on aresult of the decoding. The decoder 120 provides a bit line selectionsignal BS to the bit line selection circuit 130, based on the decodingresult. The bit line selection signal BS may be a signal for selecting abit line corresponding to the target PUF cell from among the pluralityof bit lines BL1 to BL8.

The bit line selection circuit 130 receives the bit line selectionsignal BS from the decoder 120 and controls the plurality of bit linesBL1 to BL8 based on the received bit line selection signal BS. Forexample, it is assumed that the bit line selection signal BS correspondsto the third bit line BL3. In this case, the bit line selection circuit130 outputs a signal (e.g., a current) received through the third bitline BL3 as a target current I_tg and outputs a sum of signals (e.g.,currents) received from the remaining bit lines BL1, BL2, and BL4 to BL8as a sum current I_sum.

The bit determiner 140 receives the target current I_tg and the sumcurrent I_sum. The bit determiner 140 determines the target bit TB ofthe target PUF cell based on the target current I_tg and the sum currentI_sum. For example, the bit determiner 140 may divide the sum currentI_sum by a given value. In an exemplary embodiment, the given value is avalue (e.g., N−1) that is obtained by subtracting “1” from the number ofPUF cells PC connected to one word line. That is, as described above, inthe case where the target current I_tg is provided from one of PUF cellsPC connected with the third bit line BL3 and the sum current I_sum isprovided from PUF cells PC (i.e., 7 PUF cells PC) connected with thefirst, second, and fourth to eighth bit lines BL1, BL2, and BL4 to BL8,the sum current I_sum is divided by “7”. That is, the bit determiner 140calculates an average current of a unit PUF cell based on the sumcurrent I_sum.

The bit determiner 140 compare magnitudes of the calculated averagecurrent and the target current I_tg and determines the target bit TB ofthe target PUF cell depending on a result of the comparison.

The voltage regulator 150 provides a voltage “V” to be applied to theplurality of word lines WL1 to WL8 to the decoder 120. In an exemplaryembodiment, bias voltages or active voltages (or bias currents)respectively to be provided to the plurality of word lines WL1 to WL8have the same level. Alternatively, bias voltages or active voltagesrespectively to be provided to the plurality of word lines WL1 to WL8vary depending on physical characteristics of the plurality of PUF cellsPC. Alternatively, bias voltages or active voltages respectively to beprovided to the plurality of word lines WL1 to WL8 may have differentlevels such that information collected from the plurality of PUF cellsPC form a normal distribution or a Gaussian distribution.

FIG. 4 is a diagram illustrating an exemplary structure of a pluralityof PUF cells of FIG. 3 . Referring to FIGS. 3 and 4 , any one PUF cellPCa of the plurality of PUF cells PC includes a first transistor TR1. Agate of the first transistor TR1 is connected with a word line WL, adrain thereof is connected with a bit line BL, and a source thereof isconnected to receive a particular voltage level. The first transistorTR1 may control the magnitude of a current output to the bit line BLdepending on a level of the word line WL. In this case, the magnitude ofthe current may vary depending on a physical characteristic of the firsttransistor TR1. That is, even though the plurality of PUF cells PC areformed in the same structure as “PCa” and the same word line bias isapplied to each of the plurality of PUF cells PC, a current flowingthrough the bit line BL may vary depending on a physical characteristicof each PUF cell.

Alternatively, any one PUF cell PCb of the plurality of PUF cells PCincludes first and second transistors TR1 and TR2. The first and secondtransistors TR1 and TR2 are connected in series between a node providingthe particular voltage level and the bit line BL and may operatedepending on a level of the word line WL. As described above, eventhough the plurality of PUF cells PC are formed in the same structure as“PCb” and the same word line bias is applied to each of the plurality ofPUF cells PC, a current flowing through the bit line BL may varydepending on a physical characteristic of each PUF cell.

The transistor-based PUF cells PCa and PCb described with reference toFIG. 4 are merely for describing the inventive concept and are notintended to limit the inventive concept. The plurality of PUF cells PCmay be variously implemented using various structures as describedabove.

FIG. 5 is a diagram illustrating a configuration of a PUF cell device ofFIG. 3 according to an exemplary embodiment of the inventive concept.For brevity of illustration, an example is illustrated of the PUF cellarray 110 including first to eighth PUF cells PC1 to PC8 connected withthe first word line WL1, but the inventive concept is not limitedthereto. For example, the PUF cell array 110 may further includeadditional PUF cells connected with a plurality of word lines and aplurality of bit lines. For brevity of illustration, some components(e.g., the decoder 120 and the voltage regulator 150) are omitted.

Referring to FIGS. 3 and 5 , the PUF cell device 100 includes the PUFcell array 110, the bit line selection circuit 130, and the bitdeterminer 140. The PUF cell array 110 may include the first to eighthPUF cells PC1 to PC8. The first to eighth PUF cells PC1 to PC8 areconnected with the first word line WL1. The first to eighth PUF cellsPC1 to PC8 are connected with the first to eighth bit lines BL1 to BL8,respectively. The first to eighth PUF cells PC1 to PC8 respectivelyoutput first to eighth currents I1 to I8 through the first to eighth bitlines BL1 to BL8 in response to a first voltage V1 provided to the firstword line WL1. The first voltage V1 may be provided by the voltageregulator 150.

The bit line selection circuit 130 includes first to eighth selectorsSEL1 to SEL8. The first to eighth selectors SEL1 to SEL8 are connectedwith the first to eighth bit lines BL1 to BL8, respectively. The firstto eighth selectors SEL1 to SEL8 operate in response to bit lineselection signals BS1 to BS8 and inverted bit line selection signals/BS1 to /BS8.

For example, the first selector SEL1 includes a first transistorconfigured to provide the first current I1 output from the first bitline BL1 to a second converter 142 of the bit determiner 140 in responseto the first bit line selection signal BS1; and a second transistorconfigured to provide the first current I1 output from the first bitline BL1 to a first converter 141 of the bit determiner 140 in responseto the inverted bit line selection signal /BS1. Similar to the abovedescription, the remaining selectors SEL2 to SEL8 may also operate inresponse to the corresponding bit line selection signals BS2 to BS8 andthe corresponding inverted bit line selection signals /BS2 to /BS8, andthus, additional description is omitted to avoid redundancy.

In an exemplary embodiment, each of the bit line selection signals BS1to BS8 is a signal for selecting a bit line corresponding to a targetPUF cell, and each of the inverted bit line selection signals /BS1 to/BS8 is a signal for selecting a bit line corresponding to each of theremaining PUF cells. For example, it is assumed that the target PUF cellis the third PUF cell PC3. In this case, the third bit line selectionsignal BS3 is activated, and the first, second, and fourth to eighthinverted bit line selection signals /BS1, /BS2, and /BS4 to /BS8 areactivated. As such, the third current I3 output through the third bitline BL3 is provided to the second converter 142, and the first, second,and fourth to eighth currents output I1, I2, and I4 to I8 from thefirst, second, and fourth to eighth bit lines BL1, BL2, and BL4 to BL8are provided to the first converter 141 as the sum current I_sum.

The bit determiner 140 includes the first converter 141, the secondconverter 142, and a comparator COMP (e.g., an operational amplifier orother comparison circuit). The first converter 141 may be connected withtransistors, which operate in response to the inverted bit lineselection signals /BS1 to /BS8, from among transistors included in theplurality of selectors SEL1 to SEL8. The second converter 142 may beconnected with transistors, which operate in response to the bit lineselection signals BS1 to BS8, from among the transistors included in theplurality of selectors SEL1 to SEL8.

That is, as described above, the first converter 141 receives the sumcurrent I_sum corresponding to a sum of currents output from theremaining PUF cells other than the target PUF cell, and the secondconverter 142 receives the target current I_tg output from the targetPUF cell. The first converter 141 converts the received sum currentI_sum to output a central value CV, and the second converter 142converts the target current I_tg to output a target value TV.

In an exemplary embodiment, the central value CV and the target value TVare voltage levels respectively corresponding to the sum current I_sumand the target current I_tg. That is, the first converter 141 and thesecond converter 142 may be a current-voltage converter. However, theinventive concept is not limited thereto. For example, each of the firstand second converters 141 and 142 may be implemented with a currentmirror configured to replicate a received current at a given ratio.

In an exemplary embodiment, the first converter 141 determines thecentral value CV by dividing the sum current I_sum by a given value.That is, the first converter 141 may provide a function of a divider DIVconfigured to divide the sum current I_sum by a given value. Forexample, the first converter 141 may include a divider or dividercircuit to divide the sum current I_sum by the given value. For example,as described above, in the case where the target PUF cell is the thirdPUF cell PC3, the sum current I_sum may be a sum of currents (e.g., I1,I2, and I4 to I8) output from 7 PUF cells (e.g., PC1, PC2, and PC4 toPC8). That is, the first converter 141 may calculate a current valuecorresponding to the central value CV by dividing the sum current I_sumby “7”. In an exemplary embodiment, the central value CV indicates acentral value of a normal distribution or a Gaussian distribution thatis formed by information obtained from the plurality of PUF cells PC1 toPC8 (however, the number of PUF cells being more than 8) connected withthe first word line WL1. That is, in the case where the number of aplurality of PUF cells is a particular number or more (e.g., 4 to 256 ormore), the remaining PUF cells of the plurality of PUF cells other thanthe target PUF cell may form a normal distribution or a Gaussiandistribution, and thus, the central value CV may be calculated by usingthe remaining PUF cells.

In an exemplary embodiment, a division ratio of the first converter 141is determined based on the number of PUF cells corresponding to the sumcurrent I_sum. In an exemplary embodiment, the division ratio of thefirst converter 141 may be greater or smaller than the number of PUFcells corresponding to the sum current I_sum as much as a given value.

In an exemplary embodiment, the second converter 142 determines thetarget value TV without performing a separate division operation on thetarget current I_tg. Alternatively, the second converter 142 determinesthe target value TV by dividing the target current I_tg based on a givenratio. In an exemplary embodiment, a second division ratio of the secondconverter 142 is based on a first division ratio of the first converter141. In an exemplary embodiment, the second division ratio of the secondconverter 142 is smaller than the first division ratio of the firstconverter 141.

The comparator COMP receives the central value CV from the firstconverter 141 and receives the target value TV from the second converter142. The comparator COMP compares the central value CV and the targetvalue TV and outputs the target bit TB as a result of the comparison.

As described above, the PUF cell device 100 according to an exemplaryembodiment of the inventive concept determines the target bit TB of thetarget PUF cell by calculating the central value CV using some of theplurality of PUF cells PC without a separate analog-to-digital converterand separate reference data and comparing the calculated central valueCV and the target value TV of the target PUF cell. Accordingly, acircuit complexity of the PUF device 100 is decreased, and a PUF celldevice 100 having improved reliability may be realized.

FIG. 6 is a flowchart illustrating an operation of a PUF cell device ofFIGS. 3 and 5 according to an exemplary embodiment of the inventiveconcept. Referring to FIGS. 3, 5, and 6 , in operation S110, the PUFcell device 100 selects a target PUF cell. For example, the PUF celldevice 100 may receive the control signal CTRL from the controller 101and may select the target PUF cell of the plurality of PUF cells PCbased on the received control signal CTRL.

In operation S120, the PUF cell device 100 provides the first voltage V1to a word line corresponding to the selected target PUF cell. In anexemplary embodiment, the first voltage V1 may have a level forobtaining different magnitudes of currents from a plurality of PUF cellsconnected with the first word line WL1.

In operation S130, the PUF cell device 100 generates a central value CV.For example, as described with reference to FIG. 5 , the PUF cell device100 may obtain the sum current I_sum corresponding to a sum of currentsfrom the remaining PUF cells other than a target PUF cell from among theplurality of PUF cells connected with the word line and may generate thecentral value CV based on the obtained sum current I_sum.

In operation S140, the PUF cell device 100 compares the target value TVand the central value CV. For example, as described with reference toFIG. 5 , the target value TV may be a value corresponding to the targetcurrent I_tg obtained from the target PUF cell, and the central value CVmay be a value generated based on the sum current I_sum obtained fromthe remaining PUF cells. The PUF cell device 100 may determine whetherthe target value TV is greater than the central value CV.

When the target value TV is greater than the central value CV, inoperation S151, the PUF cell device 100 sets the target bit TB to afirst value (e.g., “bit 1”). When the target value TV is smaller thanthe central value CV, in operation S152, the PUF cell device 100 setsthe target bit TB to a second value (e.g., “bit 0”) different from thefirst value. In an exemplary embodiment, when the target value isgreater than or equal the central CV, the target bit is set to the firstvalue. In an alternate embodiment, when the target value is less than orequal the central value, the target bit is set to the second value.

In operation S160, the PUF cell device 100 outputs the determined targetbit TB.

FIG. 7 is a diagram for describing an operation of a PUF cell device ofFIG. 3 . A horizontal axis of a distribution of FIG. 7 indicatesinformation (e.g., mismatch information or the amount of current)obtained from PUF cells.

Referring to FIGS. 3 and 7 , information obtained from the plurality ofPUF cells PC included in the PUF cell device 100 may form the firstdistribution DB1. A central value of the first distribution DB1 that isthe reference value REF0 is described with reference to FIG. 2 , andthus, additional description is omitted to avoid redundancy.

In an exemplary embodiment, information obtained from the plurality ofPUF cells PC connected to the first word line WL1 forms a first subdistribution sDB1, and information obtained from the plurality of PUFcells PC connected to the second word line WL2 forms a second subdistribution sDB2. As illustrated in FIG. 7 , each of the first andsecond sub distributions sDB1 and sDB2 may have a shape of a normaldistribution or a Gaussian distribution.

That is, in the case where a first target PUF cell is selected from theplurality of PUF cells PC connected to the first word line WL1, anaverage value of information respectively obtained from the remainingPUF cells other than the target PUF cell from among the plurality of PUFcells PC connected to the first word line WL1 has a first central valueCVa. As such, whether the first target PUF cell is a positive PUF cell+PC having a positive polarity or a negative PUF cell −PC having anegative polarity may be determined by comparing a first target valuebased on information obtained from the first target PUF cell with thefirst central value CVa.

Likewise, in the case where a second target PUF cell is selected fromthe plurality of PUF cells PC connected to the second word line WL2, anaverage value of information respectively obtained from the remainingPUF cells other than the target PUF cell from among the plurality of PUFcells PC connected to the second word line WL2 has a second centralvalue CVb. As such, whether the second target PUF cell is a positive PUFcell +PC having a positive polarity or a negative PUF cell −PC having anegative polarity may be determined by comparing a second target valuebased on information obtained from the second target PUF cell with thesecond central value CVb.

As described above, the plurality of PUF cells PC included in the PUFcell device 100 of the inventive concept may form normal or Gaussiandistributions that vary depending on biases of word lines. Accordingly,the PUF cell device 100 of the inventive concept may calculate a centralvalue by using PUF cells connected to the same word line as a target PUFcell and may determine a target bit of the target PUF cell based on thecalculated central value.

FIG. 8 is a diagram for describing a target bit determining method of aPUF cell device of FIG. 3 according to an exemplary embodiment of theinventive concept. Referring to FIGS. 3 and 8 , the PUF cell device 100includes the PUF cell array 110, the bit line selection circuit 130, andthe bit determiner 140. The PUF cell array 110 includes the plurality ofPUF cells PC1 to PC8 connected to the first word line WL1 and theplurality of bit lines BL1 to BL8. The bit line selection circuit 130includes a plurality of selectors SEL1 to SEL8. The bit determiner 140includes the first and second converters 141 and 142 and the comparatorCOMP. The components are described above, and thus, additionaldescription is omitted to avoid redundancy. Also, it is assumed that thethird PUF cell PC3 is a target PUF cell.

In the case where the third PUF cell PC3 is selected as a target PUFcell, the first voltage V1 is provided to the first word line WL1connected with the third PUF cell PC3. In response to the first voltageV1 of the first word line WL1, the plurality of PUF cells PC1 to PC8output the plurality of currents I1 to I8 through the plurality of bitlines BL1 to BL8, respectively.

Because the third PUF cell PC3 is the target PUF cell, the third bitline selection signal BS3 for selecting the third bit line BL3 connectedwith the third PUF cell PC3 is activated, and the inverted bit lineselection signals /BS1, /BS2, and /BS4 to /BS8 for the remaining bitlines BL1, BL2, and BL4 to BL8 are activated. That is, in response tothe third bit line selection signal BS3, the third selector SEL3provides the third current I3 of the third bit line BL3 to the secondconverter 142 as the target current I_tg. In response to the first,second, and fourth to eighth inverted bit line selection signals /BS1,/BS2, and /BS4 to /BS8, the first, second, and fourth to eighthselectors SEL1, SEL2, and SLE4 to SEL8 provide the first, second, andfourth to eighth currents I1, I2, and I4 to I8 of the first, second, andfourth to eighth bit lines BL1, BL2, and BL4 to BL8 to the firstconverter 141 as the sum current I_sum.

The first converter 141 outputs the central value CV based on the sumcurrent I_sum, and the second converter 142 outputs the target value TVbased on the third current I3 (i.e., a target current). The comparatorCOMP compares the central value CV and the target value TV to generate atarget bit TB and outputs the target bit TB of the third PUF cell PC3.

FIG. 9 is a diagram illustrating a PUF cell array according to anexemplary embodiment of the inventive concept. Referring to FIG. 9 , aPUF cell array 110A includes a plurality of PUF cells PC, and theplurality of PUF cells PC are connected with a plurality of word linesWL1 to WL6 and a plurality of bit lines BL11 to BL18 and BL21 to BL28.In an exemplary embodiment, in the PUF cell array 110A, the number ofPUF cells, the number of word lines, or the number of bit lines is notlimited to the configuration illustrated in FIG. 9 .

Unlike the PUF cell array 110 described with reference to FIG. 2 , theplurality of PUF cells PC of the PUF cell array 110A of FIG. 9 areconnected with the bit lines BL11 to BL18 of a first group and the bitlines BL21 to BL28 of a second group. For example, the PUF cells PCconnected with the first, third, and fifth word lines WL1, WL3, and WL5are connected with the bit lines BL11 to BL18 of the first group, andthe PUF cells PC connected with the second, fourth, and sixth word linesWL2, WL4, and WL6 are connected with the bit lines BL21 to BL28 of thesecond group. That is, the PUF cells PC connected with the first, third,and fifth word lines WL1, WL3, and WL5 and the PUF cells PC connectedwith the second, fourth, and sixth word lines WL2, WL4, and WL6 areconnected with bit lines of different groups and may operateindependently of each other.

FIG. 10A is a diagram illustrating a PUF cell device to which a PUF cellarray of FIG. 9 is applied. FIGS. 10B to 10D are diagrams for describingan operation of a PUF cell device of FIG. 10A. For brief description,components that are the same as the components described above are notdescribed.

Referring to FIGS. 10A to 10D, a PUF cell device includes the PUF cellarray 110A, first and second bit line selection circuits 131 and 132,and a bit determiner (e.g., a comparator COMP). The PUF cell array 110Ainclude the plurality of PUF cells PC11 to PC18 and PC21 to PC28. Theplurality of PUF cells PC11 to PC18 and PC21 to PC28 may be connectedwith the first and second word lines WL1 and WL2. The PUF cells PC PC11to PC18 connected with the first word line WL1 are connected with thebit lines BL11 to BL18 of a first group, and the PUF cells PC21 to PC28connected with the second word line WL2 are connected with the bit linesBL21 to BL28 of a second group.

The first bit line selection circuit 131 is connected with the bit linesBL11 to BL18 of the first group. In an exemplary embodiment, the firstbit line selection circuit 131 includes selectors described withreference to FIGS. 5 and 8 . The selectors included in the first bitline selection circuit 131 are respectively connected with the bit linesBL11 to BL18 of the first group and operate in response to thecorresponding bit line selection signals or the corresponding invertedbit line selection signals. The second bit line selection circuit 132 isconnected with the bit lines BL21 to BL28 of the second group. In anexemplary embodiment, the second bit line selection circuit 132 includesselectors described with reference to FIGS. 5 and 8 . The selectorsincluded in the second bit line selection circuit 132 are respectivelyconnected with the bit lines BL21 to BL28 of the second group andoperate in response to the corresponding bit line selection signals orthe corresponding inverted bit line selection signals. For brevity ofillustration and for convenience of description, the detailedconfiguration and operation of the selectors are described above, andthus, additional description is omitted to avoid redundancy.

The first converter 141 outputs the target value TV or the central valueCV based on information (e.g., a current) received from the second bitline selection circuit 132. The second converter 142 outputs the centralvalue CV or the target value TV based on information (e.g., a current)received from the first bit line selection circuit 131.

In an exemplary embodiment, the first bit line selection circuit 131provides a target current or a sum current to the second converter 142,and the second bit line selection circuit 132 provides a sum current ora target current to the first converter 141.

For example, as illustrated in FIG. 10B, it is assumed that the PUF cellPC13 connected with the first word line WL1 is a target PUF cell. Inthis case, the first voltage V1 is applied to the first and second wordlines WL1 and WL2. In an exemplary embodiment, voltages that are appliedto the first and second word lines WL1 and WL2 may be differently setdepending on physical characteristics of the plurality of PUF cells PC11to PC18 and PC21 to PC28 connected with the first and second word linesWL1 and WL2. In response to the first voltage V1 applied to the firstand second word lines WL1 and WL2, each of the plurality of PUF cellsPC11 to PC18 and PC21 to PC28 output a corresponding current.

The first bit line selection circuit 131 provides the second converter142 with the current I13 output from the PUF cell PC13 connected withthe first word line WL1 and the third bit line BL13 of the first groupin response to the third bit line selection signal BS3. In this case,the current I13 is the target current I_tg. The second converter 142outputs the target value TV based on the target current I_tg.

In response to the inverted bit line selection signals /BS1, /BS2, and/BS4 to /BS8, the second bit line selection circuit 132 provides thefirst converter 141 with the sum current I_sum2 corresponding to a sumof currents provided through some bit lines BL21, BL22, and BL24 to BL28of the second group. The first converter 141 outputs the central valueCV based on the sum current I_sum2 provided from the second bit lineselection circuit 132. The comparator COMP compares the central value CVand the target value TV to generate a target bit TB and outputs thetarget bit TB of the third PUF cell PC3 as a comparison result.

As described above, the PUF cell device according to an exemplaryembodiment of the inventive concept calculates the central value CVbased on a sum current obtained from some of PUF cells connected with asecond word line different from a first word line corresponding to atarget PUF cell. In this case, the some PUF cells may indicate PUFcells, which are connected with remaining bit lines other than thecorresponding bit line to the target PUF cell, from among the PUF cellsconnected with the different word line. That is, in the embodiment ofFIG. 10B, in the case where the target PUF cell is connected with thethird bit line BL13 of the first group, PUF cells that are used tocalculate the central value CV are the PUF cells PC21, PC22, and PC24 toPC28 connected with the second word line WL2 and the first, second, andfourth to eighth bit lines BL21, BL22, and BL24 to BL28 of the secondgroup.

However, the inventive concept is not limited thereto. For example, asillustrated in FIG. 10C, in the case where a target PUF cell (e.g.,PC13) is connected with the first word line WL1, all the PUF cells PC21to PC28 connected with the second word line WL2 may be used to calculatethe central value CV. In this case, a target bit determining operationis similar to that described above except that the second bit lineselection circuit 132 receives the first to eighth inverted bit lineselection signals /BS1 to /BS8 and all the PUF cells PC21 to PC28connected with the second word line WL2 are used to calculate thecentral value CV, and thus, additional description is omitted to avoidredundancy.

However, the inventive concept is not limited thereto. For example, asillustrated in FIG. 10D, in the case where a target PUF cell (e.g.,PC13) is connected with the first word line WL1, all the remaining PUFcells PC11, PC12, PC14 to PC18, and PC21 to PC28 other than the targetPUF cell PC13 from among the plurality of PUF cells PC11 to PC18 andPC21 to PC28 connected with the first and second word lines WL1 and WL2are used to calculate the central value CV. In this case, the second bitline selection circuit 132 provides the first converter 141 with asecond sum current I_sum2 corresponding to a sum of currents from thePUF cells PC21 to PC28 connected with the second word line WL2, and thefirst bit line selection circuit 131 provides the first converter 141with a first sum current I_sum1 corresponding to a sum of currents fromthe remaining PUF cells PC11, PC12, and PC14 to PC18 other than thetarget PUF cell PC3 from among the PUF cells PC11 to PC18 connected withthe first word line WL1. The first converter 141 outputs the centralvalue CV based on both the first sum current I_sum1 and the second sumcurrent I_sum2.

In an exemplary embodiment, a division ratio of the first converter 141or the second converter 142 may vary depending on the number of PUFcells to be used to calculate the central value CV.

The above exemplary embodiments are provided for describing theinventive concept and are not intended to limit the inventive concept.For example, in a PUF cell device, the number of PUF cells, the numberof word lines, or the number of bit lines may be variously changed ormodified. Also, PUF cells that are used to calculate the central valueCV may be variously constructed depending on a structure of a PUF cellarray. For example, an embodiment in which a central value is calculatedby using PUF cells of a word line adjacent to a word line of a targetPUF cell is described with reference to FIGS. 10A to 10D, but PUF cellsof a word line physically spaced from a word line of a target PUF cellmay be used to calculate a central value. Alternatively, a plurality ofPUF cells connected with a plurality of word lines may be used tocalculate a central value.

FIG. 11 is a diagram for describing a way to improve reliability of aPUF cell device. Referring to FIG. 11 , as described above, informationobtained from a plurality of PUF cells of a PUF cell device may form anormal distribution or a Gaussian distribution like the firstdistribution DB1, and the target bit TB or a polarity of a PUF cell maydetermined based on the reference value REF0. Information that areoutput from PUF cells may vary depending on various conditions (e.g., anoperating temperature and an operating voltage). That is, in the PUFcell that outputs information close to the reference value REF0, theoutput information may vary depending on various factors, and thus, apolarity or a determination bit of the PUF cell may be changed. Thiscauses reliability of the PUF cell device to decrease.

As such, an exemplary PUF cell device may collect information of each ofa plurality of PUF cells included in the PUF cell device through aseparate test operation, may convert the collected information intodigital data through an analog-to-digital converter, and may discard PUFcells having information between the reference value REF0 and “−a” or“+a”. For example, PUF cells having information ranging from REF0−a toREF0+a may be discarded (or ignored). That a particular PUF cell isdiscarded means that the particular PUF cell is not selected as a targetPUF cell in a next PUF cell operation. That is, the overall reliabilityof the PUF cell device may be improved by discarding (or ignoring) PUFcells PC of relatively low reliability.

However, as described above, to discard PUF cells PC of relatively lowreliability, operations such as converting information of all PUF cellsinto digital data through an analog-to-digital converter and setting aseparate reference value REF0 are required.

The PUF cell device 100 according to an exemplary embodiment of theinventive concept determines and discards unstable PUF cells byadjusting a division ratio for the central value CV and determining atarget bit based on the adjusted division ratio.

FIG. 12A is a flowchart for describing an operation of an unstable PUFcell or a valid PUF cell of a PUF cell device of FIG. 1 according to anexemplary embodiment of the inventive concept. FIG. 12B is a diagram fordescribing an operation of an unstable PUF cell or a valid PUF cell of aPUF cell device of FIG. 1 . Referring to FIGS. 1, 2, 12A, and 12B, inoperation S211, the PUF cell device 100 selects a target PUF cell. Forexample, the PUF cell device may select a target PUF cell based on areceived control signal.

In operation S212, the PUF cell device 100 generates the target value TVand generates a first central value CV1 based on a first division ratio“N−a”. In an exemplary embodiment, “N” is a positive integer, and “a” isa real number. For example, the PUF cell device 100 may generate thetarget value TV corresponding to the target PUF cell and the firstcentral value CV1 based on the operation method described with referenceto FIGS. 1 to 10D. In this case, a division ratio for the first centralvalue CV1 may be smaller than a given division ratio. For example, inthe case where a central value is calculated by using “N” PUF cells, inthe above embodiments, a 0-th central value CV0 is calculated based on adivision ratio of “N”. However, in operation S212, in the case ofcalculating a central value by using the “N” PUF cells, the centralvalue is calculated based on a division ratio of “N−a” (i.e., a divisionratio smaller than in the above embodiments). In this case, asillustrated in FIG. 12B, the first central value CV1 calculated based onthe division ratio of “N−a” is greater than the 0-th central value CV0calculated based on the division ratio of “N”.

In operation S213, the PUF cell device 100 compares the target value TVand the first central value CV1. When the target value TV is not greaterthan the first central value CV1, the PUF cell device 100 proceeds tooperation S215. When the target value TV is greater than the firstcentral value CV1, in operation S214, the PUF cell device 100 decidesthe selected target PUF cell as a valid PUF cell. For example, asillustrated in FIG. 12B, that the target value TV is greater than thefirst central value CV1 may mean that the target value TV is spaced fromthe 0-th central value CV0 a certain distance (e.g., a logicaldistance). That is, even though information output from the target PUFcell varies depending on various ambient conditions, the probabilitythat the target value TV of the target PUF cell is lower than the 0-thcentral value CV0 may be very low. That is, the target PUF cell havingthe target value TV greater than the first central value CV1 is a stable(or valid) PUF cell.

When it is determined after operation S214 or in operation S213 that thetarget value TV is not greater than the first central value CV1, inoperation S215, the PUF cell device 100 determines whether the aboveoperation has been completely performed on all the PUF cells. When it isdetermined that the above operation has not been completely performed onall the PUF cells, in operation S216, the PUF cell device 100 selects anext target PUF cell. Afterwards, the PUF cell device 100 may repeatoperation S212 to operation S216.

As described above, by performing operation S211 to operation S216, thePUF cell device 100 of the inventive concept calculates the firstcentral value CV1 (i.e., greater than the 0-th central value) by using adivision ratio smaller than a given division ratio and decides PUF cellshaving a target value greater than the first central value CV1 as validPUF cells.

In operation S221, the PUF cell device 100 selects a target PUF cell. Inoperation S222, the PUF cell device 100 generates the target value TVand generates a second central value CV2 based on a second divisionratio “N+a”. For example, the PUF cell device 100 generates the targetvalue TV corresponding to the target PUF cell and the second centralvalue CV2 based on the operation method described with reference toFIGS. 1 to 10D. In this case, as described above, in the case where acentral value is calculated by using “N” PUF cells, the 0-th centralvalue CV0 is calculated based on the division ratio of “N”. In contrast,in operation S222, the second central value CV2 is calculated based onthe division ratio of “N+a” greater than the division ratio of “N”. Inthis case, the second central value CV2 is smaller than the 0-th centralvalue CV0 as illustrated in FIG. 12B.

In operation S223, the PUF cell device 100 determines whether the targetvalue TV is smaller than the second central value CV2.

When the target value TV is not smaller than the second central valueCV2, the PUF cell device 100 proceeds to operation S225. When the targetvalue TV is smaller than the second central value CV2, in operationS224, the PUF cell device 100 decides the selected target PUF cell as avalid PUF cell. For example, as illustrated in FIG. 12B, that the targetvalue TV is smaller than the second central value CV2 means that thetarget value TV is spaced from the 0-th central value CV0 a certaindistance (e.g., a logical distance). That is, even though informationoutput from the target PUF cell varies depending on various ambientconditions, the probability that the target value TV of the target PUFcell is higher than the 0-th central value CV0 may be very low. That is,the target PUF cell having the target value TV smaller than the secondcentral value CV2 may be a stable (e.g., a valid) PUF cell.

Afterwards, the PUF cell device 100 may perform operation S225 andoperation S226. Operation S225 and operation S226 are similar tooperation S215 and operation S216 described above, and thus, additionaldescription is omitted to avoid redundancy.

As described above, by performing operation S221 to operation S226, thePUF cell device 100 of an inventive concept calculates the secondcentral value CV2 (i.e., smaller than the 0-th central value) by using adivision ratio greater than a given division ratio and may decide PUFcells having a target value smaller than the second central value CV2 asvalid PUF cells.

Afterwards, in operation S230, the PUF cell device 100 storesinformation about valid PUF cells. For example, the PUF cell device 100may store address information about valid PUF cells. In this case,because the stored information is simply address information of validPUF cells and other information about polarities or target values of thevalid PUF cells (i.e., information capable of deciding a bit value) isnot separately stored, even if the address information is leaked out orhacked, it is not possible to restore a target value or a security key.

For brevity of illustration and convenience of description, operationS230 is separately illustrated, but the inventive concept is not limitedthereto. For example, operation S230 may be individually performed inoperation S214 or operation S224. Alternatively, operation S230 may beperformed by the controller 101. For example, depending on a result ofoperation S213, a first value or a second value may be output as thetarget bit TB of the target PUF cell. The controller 101 may decide atarget PUF cell as a valid PUF cell when receiving a first valueindicating that the target value TV is greater than the first centralvalue CV1 and does not perform a separate determination on the targetPUF cell when receiving a second value indicating that the target valueTV is smaller than the first central value CV1. In an exemplaryembodiment, information (e.g., address information) about a target PUFcell used to determine the target PUF cell as a valid PUF cell is storedin a separate memory of the controller 101.

In an exemplary embodiment, PUF cells, which are not decided as validPUF cells, from among the plurality of PUF cells may be managed asinvalid PUF cells as illustrated in FIG. 12B. In an exemplaryembodiment, invalid PUF cells may indicate PUF cells not selected as atarget PUF cell in a target bit determining operation of the PUF celldevice 100 afterward.

FIGS. 13A and 13B are diagrams for describing an operation according tothe flowchart of FIG. 12A. Referring to FIGS. 1, 2 13A, and 13B, the PUFcell device 100 includes the PUF cell array 110, the bit line selector130, and the bit determiner 140. The PUF cell array 110 includes theplurality of PUF cells PC1 to PC8 connected to the first word line WL1and the plurality of bit lines BL1 to BL8. The bit line selector 130includes a plurality of selectors SEL1 to SEL8. The bit determiner 140includes the first converter 141, the second converter 142, and thecomparator COMP. Each component is described above, and thus, additionaldescription are omitted to avoid redundancy.

First, operation S211 to operation S214 of FIG. 12A are described withreference to FIG. 13A. As illustrated in FIG. 13A, the third PUF cellPC3 is selected as a target PUF cell. In this case, as in the abovedescription given with reference to FIG. 8 , the first voltage V1 isprovided to the first word line WL1, and the first, second, and fourthto eighth selectors SEL1, SEL2, and SEL4 to SEL8 provide the firstconverter 141 with the sum current I_sum corresponding to a sum of thecurrents I1, I2, and I4 to I8 of the corresponding bit lines BL1, BL2,and BL4 to BL8 in response to the corresponding inverted bit lineselection signals /BS1, /BS2, and /BS4 to /BS8. In response to the thirdbit line selection signal BS3, the third selector SEL3 provides thethird current I3 of the third bit line BL3 to the second converter 142as a target current.

As described with reference to operation S212 of FIG. 12A, the firstconverter 141 outputs the first central value CV1 based on the firstdivision ratio (e.g., “N−a”). The second converter 142 outputs thetarget value TV based on the third current I3. The comparator COMPcompares the first central value CV1 and the target value TV to generatea first classification result CR1 and outputs the first classificationresult CR1.

When a value of the first classification result CR1 is the first value(i.e., when the target value TV is greater than the first central valueCV1), the third PUF cell PC3 is decided as a valid PUF cell. In thiscase, in the distribution of FIG. 12B, the third PUF cell PC3 may beunderstood as having a value greater than the first central value CV1.

When the value of the first classification result CR1 is the secondvalue (i.e., when the target value TV is not greater than the firstcentral value CV1), the third PUF cell PC3 may be decided as a valid PUFcell or an invalid/unstable PUF cell. For example, as understood fromthe distribution of FIG. 12B, when the target value TV is not greaterthan the first central value CV1, the third PUF cell PC3 may be aninvalid/unstable PUF cell or a valid/stable PUF cell. In this case,whether the third PUF cell PC3 is a valid PUF cell is not determined.

Valid PUF cells having a target value greater than the first centralvalue CV1 from among the plurality of PUF cells PC1 to PC8 may bedecided by performing the operation described with reference to FIG. 13Aon each of the plurality of PUF cells PC1 to PC8.

Next, operation S221 to operation S224 of FIG. 12A are described withreference to FIG. 13B. As illustrated in FIG. 13B, the fourth PUF cellPC4 may be selected as a target PUF cell. In this case, each of theplurality of selectors SEL1 to SEL8 may operate in response to thecorresponding bit line selection signal or the corresponding invertedbit line selection signal. The operation of the plurality of selectorsSEL1 to SEL8 is similar to the operation described above, and thus,additional description will be omitted to avoid redundancy.

Through the operation of the plurality of selectors SEL1 to SEL8, thesum current I_sum corresponding to a sum of the remaining currents otherthan the fourth current I4 from among the plurality of currents I1 to I8is provided to the first converter 141, and the fourth current I4 isprovided to the second converter 142. The second converter 142 outputsthe target value TV based on the fourth current I4.

Unlike the above description with respect to FIG. 13A, the firstconverter 141 output the second central value CV2 based on the seconddivision ratio (e.g., “N+a”). The comparator COMP compares the secondcentral value CV2 and the target value TV to generate a secondclassification result CR2 and outputs the second classification resultCR2.

When a value of the second classification result CR2 is the second value(i.e., when the target value TV is smaller than the second central valueCV2), the fourth PUF cell PC4 is decided as a valid PUF cell. In thiscase, in the distribution of FIG. 12B, the fourth PUF cell PC4 may beunderstood as having a value smaller than the second central value CV2.

In an exemplary embodiment, valid PUF cells having a target valuesmaller than the second central value CV2 from among the plurality ofPUF cells PC1 to PC8 may be decided by performing the operationdescribed with reference to FIG. 13B on each of the plurality of PUFcells PC1 to PC8.

In an exemplary embodiment, in the case where the operation describedwith reference to FIG. 13A is first performed, the operation describedwith reference to FIG. 13B may be selectively performed depending on aresult of the operation described with reference to FIG. 13A. Forexample, the operation described with reference to FIG. 13B may beperformed only on PUF cells not decided as valid PUF cells in theoperation described with reference to FIG. 13A. Alternatively, in thecase where the operation described with reference to FIG. 13B is firstperformed, the operation described with reference to FIG. 13A may beperformed only on PUF cells not decided as valid PUF cells in theoperation described with reference to FIG. 13B.

While the operation of deciding valid PUF cells having a target valuegreater than the first central value CV1 and the operation of decidingvalid PUF cells having a target value smaller than the second centralvalue CV2 are separately illustrated and described, the inventiveconcept is not limited thereto. For example, the first converter 141 maysimultaneously calculate the first central value CV1 based on the firstdivision ratio and the second central value CV2 based on the seconddivision ratio through one conversion operation, and the comparator COMPmay simultaneously compare the first and second central values CV1 andCV2 and the target value TV. In this case, whether a target PUF cell isa valid PUF cell may be determined through one sensing operation.

In an exemplary embodiment, whether a target PUF cell is a valid PUFcell may be determined by the controller 101. For example, thecontroller 101 may perform the operation described with reference toFIG. 13A on each of a plurality of PUF cells of the PUF cell device 100and may receive a first comparison result (or a first target bit) ofeach of the plurality of PUF cells. Afterwards, the controller 101 mayperform the operation described with reference to FIG. 13B on each ofthe plurality of PUF cells of the PUF cell device 100 and may receive asecond comparison result (or a second target bit) of each of theplurality of PUF cells. The controller 101 may decide valid PUF cells bycombining the first comparison results (or the first target bits) andthe second comparison results (or the second target bits) and may storeaddress information of the decided valid PUF cells.

FIG. 14 is a block diagram illustrating a controller of FIG. 1 accordingto an exemplary embodiment of the inventive concept. Referring to FIGS.1 and 14 , the controller 101 includes a target PUF cell selectioncircuit 101 a, a memory 101 b, a security key generator 101 c (e.g., acircuit), and a control circuit 101 d.

The target PUF cell selection circuit 101 a selects a target PUF cell ofa plurality of PUF cells included in the PUF cell device 100. The targetPUF cell selection circuit 101 a may output the control signal CTRLbased on the selected target PUF cell. In an exemplary embodiment, thetarget PUF cell selection circuit 101 a is configured to select a targetPUF cell of valid PUF cells described with reference to FIGS. 12A to13B. For example, the memory 101 b may include information (e.g.,address information) about the valid PUF cells generated through theoperations described with reference to FIGS. 12A to 13B. The target PUFcell selection circuit 101 a may select a target PUF cell of the validPUF cells based on the information stored in the memory 101 b.

The security key generator 101 c receives the target bit TB from the PUFcell device 100. In an exemplary embodiment, the security key generator101 c generates a security key KEY by combining a plurality of targetbits TB received from the PUF cell device 100. The generated securitykey KEY may be provided to an external electronic device or integratedcircuit. The control circuit 101 d may be configured to control overalloperations of the controller 101. The security key KEY may be used toauthenticate the PUF cell device 100.

FIG. 15 is a diagram for describing an operation of a PUF cell deviceaccording to an exemplary embodiment of the inventive concept. Forconvenience of description, an operation based on FIG. 15 will bedescribed with reference to the PUF cell device 100 of FIG. 3 and thecontroller 101 of FIG. 14 . Also, it is assumed that the third, fifth,and eighth PUF cells PC3, PC5, and PC8 of the plurality of PUF cells PC1to PC8 are decided as valid PUF cells through the operations describedwith reference to FIGS. 12A to 13B. That is, the controller 101 of FIG.14 may include information about the valid PUF cells PC3, PC5, and PC8.

Referring to FIGS. 1, 14, and 15 , the PUF cell device 100 includes thePUF cell array 110, the bit line selection circuit 130, and the bitdeterminer 140. The PUF cell array 110 includes the plurality of PUFcells PC1 to PC8 connected to the first word line WL1 and the pluralityof bit lines BL1 to BL8. The bit line selection circuit 130 includes aplurality of selectors SEL1 to SEL8. The bit determiner 140 includes thefirst converter 141, the second converter 142, and the comparator COMP.The components are described above, and thus, additional description areomitted to avoid redundancy.

Unlike an embodiment described above, in the embodiment of FIG. 15 , thecentral value CV is calculated by using some of a plurality of PUF cellsconnected with a word line of a target PUF cell. For example, in thecase where the target PUF cell is the third PUF cell PC3, PUF cells(i.e., invalid/unstable PUF cells), which are not valid PUF cells, fromamong the plurality of PUF cells PC1 to PC8 connected with the firstword line WL1 are used as PUF cells that are used to calculate thecentral value CV. The invalid PUF cells are PUF cells adjacent to the0-th central value CV0 as described with reference to FIG. 12B. That is,in the case of calculating the central value CV by using invalid PUFcells, a value more approximate to the 0-th central value CV0 may beobtained. Also, as the number of PUF cells to be used to calculate thecentral value CV decreases, the total power consumption of the PUF celldevice 100 may be reduced. For example, in FIG. 15 , the PUF cells PC1,PC2, PC4, PC6, and PC7 are the invalid PUF cells used to generate thesum current I_sum.

FIG. 16A is a block diagram for describing an operation of a securitydevice according to an exemplary embodiment of the inventive concept,and FIGS. 16B and 16C are flowcharts for describing an operation of asecurity device according to exemplary embodiments of the inventiveconcept. Referring to FIGS. 16A and 16B, a security device 200 includesa PUF cell array 210, an analog-to-digital converter 220, and a memory230. In an exemplary embodiment, the PUF cell array 210 is a PUF celldevice or a PUF cell array described with reference to FIGS. 1 to 15 .

An operation of the security device 200 of FIG. 16A is described withreference to FIG. 16B. In operation S310 of FIG. 16B, the securitydevice 200 obtains a sensing value of each of a plurality of PUF cellsincluded in the PUF cell array 210. The sensing value may be analoginformation obtained from each of the plurality of PUF cells.

In operation S320, the security device 200 converts the sensing valuesSV into a digital value DV and stores the converted digital value DV inthe memory 230.

In operation S330, the security device 200 decides valid PUF cells basedon the digital value DV stored in the memory 230. For example, asdescribed with reference to FIG. 11 , the security device 200 may decidePUF cells corresponding to a digital value greater or smaller than thereference value REF0 as much as a given magnitude from among the digitalvalues DV as valid PUF cells. In an exemplary embodiment, informationabout the valid PUF cells may be stored in the memory 230.

In operation S340, the security device 200 performs a bit determiningoperation on each of the valid PUF cells by using a central value thatis based on invalid PUF cells. For example, the security device 200 mayperform the operation described with reference to FIG. 15 based oninformation about invalid PUF cells.

In an exemplary embodiment, the security device 200 performs a targetbit determining operation described with reference to FIGS. 1 to 15 byusing the analog-to-digital converter 220. For example, referring toFIGS. 16A and 16C, in operation S410, the security device 200 obtains asensing value from each PUF cell. In an exemplary embodiment, thesecurity device 200 obtain sensing values with regard to all the PUFcells. Alternatively, the security device 200 may obtain sensing valuesfrom a target PUF cell and PUF cells (e.g., PUF cells used to calculatea central value as described with reference to FIGS. 1 to 15 )associated with the target PUF cell.

In operation S420, the security device 200 converts the obtained sensingvalues into digital values.

In operation S430, the security device 200 may calculate the centralvalue CV. For example, as in the above description, the security device200 calculates a central value based on digital values corresponding toother PUF cells associated with a target PUF cell. That is, unlike theabove embodiments, the security device 200 obtains digital values ofother PUF cells associated with target PUF cells and calculates acentral value based on the obtained digital values, using theanalog-to-digital converter 220.

Afterwards, the security device 200 performs operation S440 to operationS460. In an exemplary embodiment, a substantial operation principle maybe similar to the above embodiments of FIG. 6 except that operations ofcalculating the central value CV and determining a target bit areperformed after analog-to-digital conversion using the analog-to-digitalconverter 220. For example, operation S440 is performed after operationS430, and may be implemented by operation S140 of FIG. 6 , operationS451 is performed when operation S440 determines that the target valueis greater than the central value CV and may be implemented by operationS151 of FIG. 6 , operation S452 is performed when operation S440determines that the target value is not greater than the central valueCV and may be implemented by operation S152, and operation S460 may beperformed thereafter and be implemented by operation S160.

As described above, the security device 200 receives the sensing valuesSV of the plurality of PUF cells from the PUF cell array 210. Thesecurity device 200 may convert the sensing values SV of the pluralityof PUF cells into the digital values DV through the analog-to-digitalconverter 220. The digital values DV may be stored in the memory 230 ora separate storage circuit. The security device 200 may calculate thecentral value CV based on digital values corresponding to at least twoor more of the remaining PUF cells other than a target PUF cell fromamong the digital values DV. In an exemplary embodiment, wheneverdetermining a target bit, the security device 200 may perform thefollowing operations on associated other PUF cells: an operation ofobtaining a sensing value and an operation of converting a sensing valueinto a digital value. Alternatively, a digital value of each of aplurality of PUF cells may be stored in the memory 230, and the securitydevice 200 may calculate a central value by using the digital valuesstored in the memory 230.

FIG. 17 is a block diagram illustrating an electronic system to which asecurity device according to an embodiment of the inventive concept isapplied. Referring to FIG. 17 , an electronic system 1000 includes ahost 1100 (e.g., a host device) and a security device 1200. Theelectronic system 1000 may be an electronic device such as a portablecommunication terminal, a personal digital assistant (PDA), a portablemultimedia player (PMP), a smartphone, a digital camera, or a wearabledevice.

The host 1100 may be configured to control the security device 1200. Thesecurity device 1200 includes a PUF cell array 1210 and may beconfigured to operate under control of the host 1100. In an exemplaryembodiment, the security device 1200 is a smart card such as anintegrated circuit (IC) card or a chip card or may be a hardwarecomponent separately provided to generate a security key.

For example, the host 1100 may receive a device identifier (ID) from thesecurity device 1200. The host 1100 may transmit a challenge to thesecurity device 1200 based on the received device identifier ID. Thesecurity device 1200 may transmit a response to the host 1100 inresponse to the challenge from the host 1100. In an exemplaryembodiment, the response includes the security key KEY described withreference to FIGS. 1 to 16 . That is, depending on the operation methoddescribed with reference to FIGS. 1 to 16 , the security device 1200 mayobtain data, which is based on the challenge from the host 1100, from aplurality of PUF cells included in the PUF cell array 1210, may generatethe response (i.e., a security key) based on the obtained data, and maytransmit the response to the host 1100. The host 1100 may perform anauthentication operation on the security device 1200 or any otherdevices based on the received response (e.g., on the security key).

FIG. 18 is a block diagram illustrating an electronic device to which asecurity device according to an exemplary embodiment of inventiveconcept is applied. Referring to FIG. 18 , an electronic device 3000includes a main processor 3100, a touch panel 3200, a touch driverintegrated circuit 3202, a display panel 3300, a display driverintegrated circuit 3302, a system memory 3400, a storage device 3500, animage processor 3800, a communication block 3700, an audio processor3600, and a security chip 3900. In an exemplary embodiment, theelectronic device 3000 may be one of various electronic devices such asa portable communication terminal, a personal digital assistant (PDA), aportable media player (PMP), a digital camera, a smartphone, a tabletcomputer, a laptop computer, and a wearable device.

The main processor 3100 may control overall operations of the electronicdevice 3000. The main processor 3100 may control/manage operations ofthe components of the electronic device 3000. The main processor 3100may process various operations for the purpose of operating theelectronic device 3000.

The touch panel 3200 may be configured to sense a touch input from auser under control of the touch driver integrated circuit 3202. Thedisplay panel 3300 may be configured to display image information undercontrol of the display driver integrated circuit 3302.

The system memory 3400 may store data that are used for an operation ofthe electronic device 3000. For example, the system memory 3400 mayinclude a volatile memory such as a static random access memory (SRAM),a dynamic RAM (DRAM), or a synchronous DRAM (SDRAM), and/or anonvolatile memory such as a phase-change RAM (PRAM), amagneto-resistive RAM (MRAM), a resistive RAM (ReRAM), or aferroelectric RAM (FRAM).

The storage device 3500 may store data regardless of whether power issupplied. For example, the storage device 3500 may include at least oneof various nonvolatile memories such as a flash memory, a PRAM, an MRAM,a ReRAM, and a FRAM. For example, the storage device 3500 may include anembedded memory and/or a removable memory of the electronic device 3000.

The audio processor 3600 may process an audio signal by using an audiosignal processor 3610. The audio processor 3600 may receive an audioinput through a microphone 3620 or may provide an audio output through aspeaker 3630.

The communication block 3700 may exchange signals with an externaldevice/system through an antenna 3710. A transceiver 3720 and amodulator/demodulator (MODEM) 3730 of the communication block 3700 mayprocess signals exchanged with the external device/system in compliancewith at least one of various wireless communication protocols: long termevolution (LTE), worldwide interoperability for microwave access(WiMax), global system for mobile communication (GSM), code divisionmultiple access (CDMA), Bluetooth, near field communication (NFC),wireless fidelity (Wi-Fi), and radio frequency identification (RFID).

The image processor 3800 may receive light through a lens 3810. An imagedevice 3820 and an image signal processor 3830 included in the imageprocessor 3800 may generate image information about an external object,based on the received light.

The security chip 3900 may be implemented to manage a security operationor an authentication operation associated with the electronic device3000. In an exemplary embodiment, the security chip 3900 includes a PUFcell device or a security device described with reference to FIGS. 1 to16 .

In an exemplary embodiment, a part of the components of FIG. 18 may beimplemented in the form of a system on chip and may be provided as anapplication processor (AP) of the electronic device 3000.

According to at least one embodiment of the inventive concept, a centralvalue is calculated by using other PUF cells associated with a targetPUF cell without separate reference data, and a target bit of the targetPUF cell is decided based on the calculated central value. Accordingly,an analog-to-digital converter or reference data is not separatelyrequired. This means that circuit complexity of a security devicedecreases. Also, because a central value optimized for each PUF cell isdecided, the reliability of the security device may be improved.

Accordingly, a security device including physical unclonable function(PUF) cells having improved reliability and reduced costs, an operationmethod of the security device, and an operation method of a physicalunclonable function cell device are provided.

While the inventive concept has been described with reference toexemplary embodiments thereof, it will be apparent to those of ordinaryskill in the art that various changes and modifications may be madethereto without departing from the spirit and scope of the inventiveconcept.

1.-20. (canceled)
 21. An operation method of a physical unclonablefunction (PUF) cell device including a plurality of PUF cells, themethod comprising: selecting a first target PUF cell of the plurality ofPUF cells; applying a first voltage to a first word line connected withthe first target PUF cell; generating a first target value based on afirst target current corresponding to the first target PUF cell andgenerating a first central value based on a first sum currentcorresponding to a sum of first currents output from first PUF cells,connected with the first word line, of the plurality of PUF cells;determining a first target bit of the first target PUF cell based on thefirst target value and the first central value; and generating asecurity key based on the first target bit for responding to anauthentication request.
 22. The method of claim 20, wherein the firsttarget PUF cell outputs the first target current in response to thefirst voltage provided through the first word line, and the first PUFcells output the first currents in response to the first voltageprovided through the first word line, respectively.
 23. The method ofclaim 20, wherein the first central value is generated based on a givenratio and a magnitude of the first sum current.
 24. The method of claim20, wherein the given ratio corresponds to the number of the first PUFcells.
 25. The method of claim 20, wherein the plurality of PUF cellsinclude a plurality of valid PUF cells and a plurality of invalid PUFcells, and the first target PUF cells is selected from the plurality ofvalid PUF cells.
 26. The method of claim 20, further comprises:selecting a second target PUF cell of the plurality of PUF cells;applying the first voltage to the first word line connected the secondtarget PUF cell; generating a second target value based on a secondtarget current corresponding to the second target PUF cell andgenerating a second central value based on a second sum currentcorresponding to a sum of second currents output from second PUF cells,connected with the first word line, of the plurality of PUF cells; anddetermining a second target bit of the second target PUF cell based onthe second target value and the second central value.
 27. The method ofclaim 20, wherein the second central value is different from the firstcentral value.
 28. The method of claim 20, wherein the first target PUFcell is one of the second PUF cells, and the second target PUF cell isone of the first PUF cells.
 29. The method of claim 20, wherein thedetermining of the first target bit comprises: setting the first targetbit to a first value when the first target value is greater than thefirst central value and setting to the first target bit to a secondvalue when the first target value is not greater than the first centralvalue, wherein the determining of the second target bit comprises:setting the second target bit to the first value when the second targetvalue is greater than the second central value and setting the secondtarget bit to the second value when the second target value is notgreater than the second central value.
 30. The method of claim 20,further comprises: selecting a third target PUF cell of the plurality ofPUF cells; applying the first voltage a second word line connected thethird target PUF cell; generating a third target value based on a thirdtarget current corresponding to the third target PUF cell and generatinga third central value based on a third sum current corresponding to asum of third currents output from third PUF cells, connected with thesecond word line, of the plurality of PUF cells; and determining a thirdtarget bit of the third target PUF cell based on the third target valueand the third central value.
 31. The method of claim 30, wherein thefirst central value is different from the third central value.
 32. Themethod of claim 20, further comprises: applying the first voltage to asecond word line different from the first word line, wherein the firstcentral value is generated based on the first sum current and a fourthsum current, and the fourth sum current corresponds to a sum of fourthcurrents output from fourth PUF cells, connected with the second wordline, of the plurality of PUF cells.
 33. An operation method of aphysical unclonable function (PUF) cell device including first to N-thPUF cells, the method comprising: applying a first voltage to a firstword line connected with the first to N-th PUF cells; obtaining firstinformation from the first PUF cell and obtaining second informationfrom the second to N-th PUF cells; determining a first bit of the firstPUF cell from the obtained first information and the obtained secondinformation; applying the first voltage to the first word line connectedwith the first to N-th PUF cells; obtaining third information from thesecond PUF cell and obtaining fourth information from the first andthird to N-th PUF cells; determining a second bit of the second PUF cellbased on the obtained third and fourth information; and generating asecurity key based on the first bit and the second bit for responding toan authentication request, wherein N is a positive integer.
 34. Themethod of claim 33, wherein the first to N-th PUF cells are respectivelyconnected with first to N-th bit lines, wherein the first to N-th PUFcells respectively output first to N-th currents through the first toN-th bit lines in response to the first voltage.
 35. The method of claim34, wherein first information corresponds to the first current, and thesecond information corresponds to a value obtained by dividing a firstsum current corresponding to a sum of the second to N-th currents by agiven division ratio, and wherein the third information corresponds tothe second current, and the fourth information corresponds to a valueobtained by dividing a second sum current corresponding to a sum of thefirst and third to N-th currents by the given division ratio.
 36. Themethod of claim 35, wherein the given division ratio corresponds to avalue of (N−1).
 37. The method of claim 34, wherein the firstinformation is a first digital value corresponding to the first current,wherein the second information is a first central value of second toN-th digital values respectively corresponding to the second to N-thcurrents, wherein the third information is a second digital valuecorresponding to the second current, and wherein the fourth informationis a second central value of the first and third to N-th digital valuesrespectively corresponding to the first and third to N-th currents. 38.The method of claim 33, wherein the determining of the first bitcomprises: determining whether the first information is greater than thesecond information; and setting the first bit to a first value when thefirst information is greater than the second information and setting thefirst bit to a second value when the first information is not greaterthan the second information, wherein the determining of the second bitcomprises: determining whether the third information is greater than thefourth information; and setting the second bit to the first value whenthe third information is greater than the fourth information and settingthe second bit to the second value when the third information is notgreater than the fourth information.
 39. An operation method of aphysical unclonable function (PUF) cell device including a plurality ofPUF cells, the method comprising: applying a first voltage to a firstword line connected with the plurality of PUF cells; obtaining firstinformation from a target PUF cell of the plurality of PUF cells andsecond information from remaining PUF cells of the plurality of PUFcells; and setting a first bit of the target PUF cell to a first valuewhen the first information is greater than the second information andsetting the first bit to a second value when the first information isnot greater than the second information.
 40. The method of claim 39,wherein the first information corresponds to a first current generatedby the target PUF cell based on the first voltage, and the secondinformation corresponds to an average of currents generated by theremaining PUF cells.